Properties

Label 966.2.f.c.461.9
Level $966$
Weight $2$
Character 966.461
Analytic conductor $7.714$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(461,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.461");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.f (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.9
Character \(\chi\) \(=\) 966.461
Dual form 966.2.f.c.461.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(0.711304 - 1.57925i) q^{3} -1.00000 q^{4} -0.334212 q^{5} +(-1.57925 - 0.711304i) q^{6} +(-0.168570 - 2.64038i) q^{7} +1.00000i q^{8} +(-1.98809 - 2.24666i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(0.711304 - 1.57925i) q^{3} -1.00000 q^{4} -0.334212 q^{5} +(-1.57925 - 0.711304i) q^{6} +(-0.168570 - 2.64038i) q^{7} +1.00000i q^{8} +(-1.98809 - 2.24666i) q^{9} +0.334212i q^{10} -0.616447i q^{11} +(-0.711304 + 1.57925i) q^{12} -3.23929i q^{13} +(-2.64038 + 0.168570i) q^{14} +(-0.237727 + 0.527806i) q^{15} +1.00000 q^{16} +3.15851 q^{17} +(-2.24666 + 1.98809i) q^{18} +0.890178i q^{19} +0.334212 q^{20} +(-4.28973 - 1.61190i) q^{21} -0.616447 q^{22} -1.00000i q^{23} +(1.57925 + 0.711304i) q^{24} -4.88830 q^{25} -3.23929 q^{26} +(-4.96219 + 1.54164i) q^{27} +(0.168570 + 2.64038i) q^{28} +2.14128i q^{29} +(0.527806 + 0.237727i) q^{30} +2.97856i q^{31} -1.00000i q^{32} +(-0.973527 - 0.438482i) q^{33} -3.15851i q^{34} +(0.0563383 + 0.882446i) q^{35} +(1.98809 + 2.24666i) q^{36} -2.08345 q^{37} +0.890178 q^{38} +(-5.11567 - 2.30412i) q^{39} -0.334212i q^{40} +5.08253 q^{41} +(-1.61190 + 4.28973i) q^{42} -11.3381 q^{43} +0.616447i q^{44} +(0.664445 + 0.750862i) q^{45} -1.00000 q^{46} -2.96029 q^{47} +(0.711304 - 1.57925i) q^{48} +(-6.94317 + 0.890178i) q^{49} +4.88830i q^{50} +(2.24666 - 4.98809i) q^{51} +3.23929i q^{52} +0.00920039i q^{53} +(1.54164 + 4.96219i) q^{54} +0.206024i q^{55} +(2.64038 - 0.168570i) q^{56} +(1.40582 + 0.633187i) q^{57} +2.14128 q^{58} +13.1251 q^{59} +(0.237727 - 0.527806i) q^{60} -8.92731i q^{61} +2.97856 q^{62} +(-5.59690 + 5.62803i) q^{63} -1.00000 q^{64} +1.08261i q^{65} +(-0.438482 + 0.973527i) q^{66} +5.51592 q^{67} -3.15851 q^{68} +(-1.57925 - 0.711304i) q^{69} +(0.882446 - 0.0563383i) q^{70} -4.57347i q^{71} +(2.24666 - 1.98809i) q^{72} -6.21012i q^{73} +2.08345i q^{74} +(-3.47707 + 7.71988i) q^{75} -0.890178i q^{76} +(-1.62765 + 0.103915i) q^{77} +(-2.30412 + 5.11567i) q^{78} -7.38606 q^{79} -0.334212 q^{80} +(-1.09498 + 8.93314i) q^{81} -5.08253i q^{82} -11.3888 q^{83} +(4.28973 + 1.61190i) q^{84} -1.05561 q^{85} +11.3381i q^{86} +(3.38163 + 1.52310i) q^{87} +0.616447 q^{88} +15.6130 q^{89} +(0.750862 - 0.664445i) q^{90} +(-8.55295 + 0.546049i) q^{91} +1.00000i q^{92} +(4.70391 + 2.11867i) q^{93} +2.96029i q^{94} -0.297508i q^{95} +(-1.57925 - 0.711304i) q^{96} -10.2696i q^{97} +(0.890178 + 6.94317i) q^{98} +(-1.38495 + 1.22555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.711304 1.57925i 0.410672 0.911783i
\(4\) −1.00000 −0.500000
\(5\) −0.334212 −0.149464 −0.0747321 0.997204i \(-0.523810\pi\)
−0.0747321 + 0.997204i \(0.523810\pi\)
\(6\) −1.57925 0.711304i −0.644728 0.290389i
\(7\) −0.168570 2.64038i −0.0637136 0.997968i
\(8\) 1.00000i 0.353553i
\(9\) −1.98809 2.24666i −0.662697 0.748887i
\(10\) 0.334212i 0.105687i
\(11\) 0.616447i 0.185866i −0.995672 0.0929329i \(-0.970376\pi\)
0.995672 0.0929329i \(-0.0296242\pi\)
\(12\) −0.711304 + 1.57925i −0.205336 + 0.455892i
\(13\) 3.23929i 0.898419i −0.893427 0.449209i \(-0.851706\pi\)
0.893427 0.449209i \(-0.148294\pi\)
\(14\) −2.64038 + 0.168570i −0.705670 + 0.0450523i
\(15\) −0.237727 + 0.527806i −0.0613808 + 0.136279i
\(16\) 1.00000 0.250000
\(17\) 3.15851 0.766051 0.383026 0.923738i \(-0.374882\pi\)
0.383026 + 0.923738i \(0.374882\pi\)
\(18\) −2.24666 + 1.98809i −0.529543 + 0.468598i
\(19\) 0.890178i 0.204221i 0.994773 + 0.102110i \(0.0325595\pi\)
−0.994773 + 0.102110i \(0.967441\pi\)
\(20\) 0.334212 0.0747321
\(21\) −4.28973 1.61190i −0.936096 0.351744i
\(22\) −0.616447 −0.131427
\(23\) 1.00000i 0.208514i
\(24\) 1.57925 + 0.711304i 0.322364 + 0.145194i
\(25\) −4.88830 −0.977660
\(26\) −3.23929 −0.635278
\(27\) −4.96219 + 1.54164i −0.954974 + 0.296689i
\(28\) 0.168570 + 2.64038i 0.0318568 + 0.498984i
\(29\) 2.14128i 0.397626i 0.980037 + 0.198813i \(0.0637086\pi\)
−0.980037 + 0.198813i \(0.936291\pi\)
\(30\) 0.527806 + 0.237727i 0.0963638 + 0.0434027i
\(31\) 2.97856i 0.534966i 0.963563 + 0.267483i \(0.0861919\pi\)
−0.963563 + 0.267483i \(0.913808\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −0.973527 0.438482i −0.169469 0.0763298i
\(34\) 3.15851i 0.541680i
\(35\) 0.0563383 + 0.882446i 0.00952290 + 0.149161i
\(36\) 1.98809 + 2.24666i 0.331349 + 0.374444i
\(37\) −2.08345 −0.342517 −0.171258 0.985226i \(-0.554783\pi\)
−0.171258 + 0.985226i \(0.554783\pi\)
\(38\) 0.890178 0.144406
\(39\) −5.11567 2.30412i −0.819163 0.368955i
\(40\) 0.334212i 0.0528436i
\(41\) 5.08253 0.793758 0.396879 0.917871i \(-0.370093\pi\)
0.396879 + 0.917871i \(0.370093\pi\)
\(42\) −1.61190 + 4.28973i −0.248721 + 0.661920i
\(43\) −11.3381 −1.72905 −0.864526 0.502589i \(-0.832381\pi\)
−0.864526 + 0.502589i \(0.832381\pi\)
\(44\) 0.616447i 0.0929329i
\(45\) 0.664445 + 0.750862i 0.0990496 + 0.111932i
\(46\) −1.00000 −0.147442
\(47\) −2.96029 −0.431803 −0.215901 0.976415i \(-0.569269\pi\)
−0.215901 + 0.976415i \(0.569269\pi\)
\(48\) 0.711304 1.57925i 0.102668 0.227946i
\(49\) −6.94317 + 0.890178i −0.991881 + 0.127168i
\(50\) 4.88830i 0.691310i
\(51\) 2.24666 4.98809i 0.314596 0.698473i
\(52\) 3.23929i 0.449209i
\(53\) 0.00920039i 0.00126377i 1.00000 0.000631885i \(0.000201135\pi\)
−1.00000 0.000631885i \(0.999799\pi\)
\(54\) 1.54164 + 4.96219i 0.209791 + 0.675269i
\(55\) 0.206024i 0.0277803i
\(56\) 2.64038 0.168570i 0.352835 0.0225262i
\(57\) 1.40582 + 0.633187i 0.186205 + 0.0838677i
\(58\) 2.14128 0.281164
\(59\) 13.1251 1.70874 0.854371 0.519663i \(-0.173942\pi\)
0.854371 + 0.519663i \(0.173942\pi\)
\(60\) 0.237727 0.527806i 0.0306904 0.0681395i
\(61\) 8.92731i 1.14302i −0.820594 0.571512i \(-0.806357\pi\)
0.820594 0.571512i \(-0.193643\pi\)
\(62\) 2.97856 0.378278
\(63\) −5.59690 + 5.62803i −0.705143 + 0.709065i
\(64\) −1.00000 −0.125000
\(65\) 1.08261i 0.134281i
\(66\) −0.438482 + 0.973527i −0.0539733 + 0.119833i
\(67\) 5.51592 0.673877 0.336938 0.941527i \(-0.390609\pi\)
0.336938 + 0.941527i \(0.390609\pi\)
\(68\) −3.15851 −0.383026
\(69\) −1.57925 0.711304i −0.190120 0.0856310i
\(70\) 0.882446 0.0563383i 0.105472 0.00673371i
\(71\) 4.57347i 0.542771i −0.962471 0.271386i \(-0.912518\pi\)
0.962471 0.271386i \(-0.0874819\pi\)
\(72\) 2.24666 1.98809i 0.264772 0.234299i
\(73\) 6.21012i 0.726840i −0.931625 0.363420i \(-0.881609\pi\)
0.931625 0.363420i \(-0.118391\pi\)
\(74\) 2.08345i 0.242196i
\(75\) −3.47707 + 7.71988i −0.401498 + 0.891414i
\(76\) 0.890178i 0.102110i
\(77\) −1.62765 + 0.103915i −0.185488 + 0.0118422i
\(78\) −2.30412 + 5.11567i −0.260891 + 0.579236i
\(79\) −7.38606 −0.830997 −0.415499 0.909594i \(-0.636393\pi\)
−0.415499 + 0.909594i \(0.636393\pi\)
\(80\) −0.334212 −0.0373661
\(81\) −1.09498 + 8.93314i −0.121664 + 0.992571i
\(82\) 5.08253i 0.561272i
\(83\) −11.3888 −1.25008 −0.625042 0.780592i \(-0.714918\pi\)
−0.625042 + 0.780592i \(0.714918\pi\)
\(84\) 4.28973 + 1.61190i 0.468048 + 0.175872i
\(85\) −1.05561 −0.114497
\(86\) 11.3381i 1.22262i
\(87\) 3.38163 + 1.52310i 0.362549 + 0.163294i
\(88\) 0.616447 0.0657135
\(89\) 15.6130 1.65498 0.827490 0.561481i \(-0.189768\pi\)
0.827490 + 0.561481i \(0.189768\pi\)
\(90\) 0.750862 0.664445i 0.0791478 0.0700386i
\(91\) −8.55295 + 0.546049i −0.896593 + 0.0572415i
\(92\) 1.00000i 0.104257i
\(93\) 4.70391 + 2.11867i 0.487773 + 0.219695i
\(94\) 2.96029i 0.305331i
\(95\) 0.297508i 0.0305237i
\(96\) −1.57925 0.711304i −0.161182 0.0725972i
\(97\) 10.2696i 1.04272i −0.853338 0.521358i \(-0.825426\pi\)
0.853338 0.521358i \(-0.174574\pi\)
\(98\) 0.890178 + 6.94317i 0.0899215 + 0.701366i
\(99\) −1.38495 + 1.22555i −0.139193 + 0.123173i
\(100\) 4.88830 0.488830
\(101\) 11.1328 1.10775 0.553875 0.832600i \(-0.313148\pi\)
0.553875 + 0.832600i \(0.313148\pi\)
\(102\) −4.98809 2.24666i −0.493895 0.222453i
\(103\) 4.70411i 0.463510i 0.972774 + 0.231755i \(0.0744468\pi\)
−0.972774 + 0.231755i \(0.925553\pi\)
\(104\) 3.23929 0.317639
\(105\) 1.43368 + 0.538715i 0.139913 + 0.0525732i
\(106\) 0.00920039 0.000893620
\(107\) 6.66683i 0.644507i −0.946653 0.322254i \(-0.895560\pi\)
0.946653 0.322254i \(-0.104440\pi\)
\(108\) 4.96219 1.54164i 0.477487 0.148345i
\(109\) 14.7101 1.40897 0.704486 0.709718i \(-0.251178\pi\)
0.704486 + 0.709718i \(0.251178\pi\)
\(110\) 0.206024 0.0196436
\(111\) −1.48196 + 3.29029i −0.140662 + 0.312301i
\(112\) −0.168570 2.64038i −0.0159284 0.249492i
\(113\) 16.9174i 1.59146i 0.605653 + 0.795729i \(0.292912\pi\)
−0.605653 + 0.795729i \(0.707088\pi\)
\(114\) 0.633187 1.40582i 0.0593034 0.131667i
\(115\) 0.334212i 0.0311655i
\(116\) 2.14128i 0.198813i
\(117\) −7.27760 + 6.44002i −0.672814 + 0.595380i
\(118\) 13.1251i 1.20826i
\(119\) −0.532431 8.33965i −0.0488079 0.764495i
\(120\) −0.527806 0.237727i −0.0481819 0.0217014i
\(121\) 10.6200 0.965454
\(122\) −8.92731 −0.808240
\(123\) 3.61523 8.02661i 0.325974 0.723735i
\(124\) 2.97856i 0.267483i
\(125\) 3.30479 0.295590
\(126\) 5.62803 + 5.59690i 0.501385 + 0.498611i
\(127\) 1.27261 0.112926 0.0564631 0.998405i \(-0.482018\pi\)
0.0564631 + 0.998405i \(0.482018\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −8.06487 + 17.9058i −0.710073 + 1.57652i
\(130\) 1.08261 0.0949513
\(131\) −3.12774 −0.273272 −0.136636 0.990621i \(-0.543629\pi\)
−0.136636 + 0.990621i \(0.543629\pi\)
\(132\) 0.973527 + 0.438482i 0.0847347 + 0.0381649i
\(133\) 2.35040 0.150058i 0.203806 0.0130116i
\(134\) 5.51592i 0.476503i
\(135\) 1.65842 0.515236i 0.142734 0.0443445i
\(136\) 3.15851i 0.270840i
\(137\) 9.47914i 0.809858i −0.914348 0.404929i \(-0.867296\pi\)
0.914348 0.404929i \(-0.132704\pi\)
\(138\) −0.711304 + 1.57925i −0.0605503 + 0.134435i
\(139\) 12.4667i 1.05741i −0.848806 0.528704i \(-0.822678\pi\)
0.848806 0.528704i \(-0.177322\pi\)
\(140\) −0.0563383 0.882446i −0.00476145 0.0745803i
\(141\) −2.10567 + 4.67505i −0.177329 + 0.393711i
\(142\) −4.57347 −0.383797
\(143\) −1.99685 −0.166985
\(144\) −1.98809 2.24666i −0.165674 0.187222i
\(145\) 0.715642i 0.0594309i
\(146\) −6.21012 −0.513953
\(147\) −3.53289 + 11.5982i −0.291388 + 0.956605i
\(148\) 2.08345 0.171258
\(149\) 11.1915i 0.916839i −0.888736 0.458420i \(-0.848416\pi\)
0.888736 0.458420i \(-0.151584\pi\)
\(150\) 7.71988 + 3.47707i 0.630325 + 0.283902i
\(151\) 15.7569 1.28228 0.641141 0.767423i \(-0.278462\pi\)
0.641141 + 0.767423i \(0.278462\pi\)
\(152\) −0.890178 −0.0722030
\(153\) −6.27941 7.09610i −0.507660 0.573686i
\(154\) 0.103915 + 1.62765i 0.00837368 + 0.131160i
\(155\) 0.995473i 0.0799583i
\(156\) 5.11567 + 2.30412i 0.409582 + 0.184478i
\(157\) 0.132472i 0.0105724i 0.999986 + 0.00528622i \(0.00168267\pi\)
−0.999986 + 0.00528622i \(0.998317\pi\)
\(158\) 7.38606i 0.587604i
\(159\) 0.0145298 + 0.00654428i 0.00115228 + 0.000518995i
\(160\) 0.334212i 0.0264218i
\(161\) −2.64038 + 0.168570i −0.208091 + 0.0132852i
\(162\) 8.93314 + 1.09498i 0.701854 + 0.0860297i
\(163\) −1.56309 −0.122430 −0.0612152 0.998125i \(-0.519498\pi\)
−0.0612152 + 0.998125i \(0.519498\pi\)
\(164\) −5.08253 −0.396879
\(165\) 0.325365 + 0.146546i 0.0253296 + 0.0114086i
\(166\) 11.3888i 0.883942i
\(167\) −9.97417 −0.771825 −0.385912 0.922535i \(-0.626113\pi\)
−0.385912 + 0.922535i \(0.626113\pi\)
\(168\) 1.61190 4.28973i 0.124360 0.330960i
\(169\) 2.50697 0.192844
\(170\) 1.05561i 0.0809618i
\(171\) 1.99993 1.76976i 0.152938 0.135337i
\(172\) 11.3381 0.864526
\(173\) −12.3935 −0.942259 −0.471129 0.882064i \(-0.656153\pi\)
−0.471129 + 0.882064i \(0.656153\pi\)
\(174\) 1.52310 3.38163i 0.115466 0.256361i
\(175\) 0.824023 + 12.9070i 0.0622902 + 0.975674i
\(176\) 0.616447i 0.0464664i
\(177\) 9.33594 20.7279i 0.701732 1.55800i
\(178\) 15.6130i 1.17025i
\(179\) 4.94693i 0.369751i 0.982762 + 0.184875i \(0.0591881\pi\)
−0.982762 + 0.184875i \(0.940812\pi\)
\(180\) −0.664445 0.750862i −0.0495248 0.0559659i
\(181\) 11.2427i 0.835661i −0.908525 0.417831i \(-0.862791\pi\)
0.908525 0.417831i \(-0.137209\pi\)
\(182\) 0.546049 + 8.55295i 0.0404758 + 0.633987i
\(183\) −14.0985 6.35003i −1.04219 0.469408i
\(184\) 1.00000 0.0737210
\(185\) 0.696313 0.0511940
\(186\) 2.11867 4.70391i 0.155348 0.344908i
\(187\) 1.94705i 0.142383i
\(188\) 2.96029 0.215901
\(189\) 4.90700 + 12.8422i 0.356931 + 0.934131i
\(190\) −0.297508 −0.0215835
\(191\) 11.5303i 0.834304i −0.908837 0.417152i \(-0.863028\pi\)
0.908837 0.417152i \(-0.136972\pi\)
\(192\) −0.711304 + 1.57925i −0.0513340 + 0.113973i
\(193\) −5.65666 −0.407175 −0.203588 0.979057i \(-0.565260\pi\)
−0.203588 + 0.979057i \(0.565260\pi\)
\(194\) −10.2696 −0.737312
\(195\) 1.70972 + 0.770067i 0.122436 + 0.0551456i
\(196\) 6.94317 0.890178i 0.495941 0.0635841i
\(197\) 3.68947i 0.262864i −0.991325 0.131432i \(-0.958042\pi\)
0.991325 0.131432i \(-0.0419575\pi\)
\(198\) 1.22555 + 1.38495i 0.0870963 + 0.0984240i
\(199\) 9.66592i 0.685199i −0.939482 0.342599i \(-0.888693\pi\)
0.939482 0.342599i \(-0.111307\pi\)
\(200\) 4.88830i 0.345655i
\(201\) 3.92350 8.71104i 0.276742 0.614430i
\(202\) 11.1328i 0.783298i
\(203\) 5.65379 0.360956i 0.396818 0.0253342i
\(204\) −2.24666 + 4.98809i −0.157298 + 0.349236i
\(205\) −1.69864 −0.118638
\(206\) 4.70411 0.327751
\(207\) −2.24666 + 1.98809i −0.156154 + 0.138182i
\(208\) 3.23929i 0.224605i
\(209\) 0.548748 0.0379577
\(210\) 0.538715 1.43368i 0.0371749 0.0989334i
\(211\) 9.28923 0.639497 0.319748 0.947503i \(-0.396402\pi\)
0.319748 + 0.947503i \(0.396402\pi\)
\(212\) 0.00920039i 0.000631885i
\(213\) −7.22268 3.25313i −0.494890 0.222901i
\(214\) −6.66683 −0.455735
\(215\) 3.78935 0.258431
\(216\) −1.54164 4.96219i −0.104896 0.337634i
\(217\) 7.86453 0.502098i 0.533879 0.0340846i
\(218\) 14.7101i 0.996293i
\(219\) −9.80737 4.41729i −0.662720 0.298493i
\(220\) 0.206024i 0.0138901i
\(221\) 10.2313i 0.688235i
\(222\) 3.29029 + 1.48196i 0.220830 + 0.0994630i
\(223\) 26.0351i 1.74344i −0.490005 0.871720i \(-0.663005\pi\)
0.490005 0.871720i \(-0.336995\pi\)
\(224\) −2.64038 + 0.168570i −0.176418 + 0.0112631i
\(225\) 9.71840 + 10.9824i 0.647893 + 0.732157i
\(226\) 16.9174 1.12533
\(227\) 1.73870 0.115401 0.0577006 0.998334i \(-0.481623\pi\)
0.0577006 + 0.998334i \(0.481623\pi\)
\(228\) −1.40582 0.633187i −0.0931026 0.0419339i
\(229\) 5.40527i 0.357190i −0.983923 0.178595i \(-0.942845\pi\)
0.983923 0.178595i \(-0.0571552\pi\)
\(230\) 0.334212 0.0220373
\(231\) −0.993648 + 2.64439i −0.0653773 + 0.173988i
\(232\) −2.14128 −0.140582
\(233\) 13.3463i 0.874345i 0.899378 + 0.437173i \(0.144020\pi\)
−0.899378 + 0.437173i \(0.855980\pi\)
\(234\) 6.44002 + 7.27760i 0.420997 + 0.475752i
\(235\) 0.989366 0.0645391
\(236\) −13.1251 −0.854371
\(237\) −5.25374 + 11.6645i −0.341267 + 0.757689i
\(238\) −8.33965 + 0.532431i −0.540579 + 0.0345124i
\(239\) 29.0538i 1.87933i −0.342093 0.939666i \(-0.611136\pi\)
0.342093 0.939666i \(-0.388864\pi\)
\(240\) −0.237727 + 0.527806i −0.0153452 + 0.0340698i
\(241\) 16.1968i 1.04333i 0.853151 + 0.521664i \(0.174688\pi\)
−0.853151 + 0.521664i \(0.825312\pi\)
\(242\) 10.6200i 0.682679i
\(243\) 13.3288 + 8.08343i 0.855046 + 0.518553i
\(244\) 8.92731i 0.571512i
\(245\) 2.32049 0.297508i 0.148251 0.0190071i
\(246\) −8.02661 3.61523i −0.511758 0.230499i
\(247\) 2.88355 0.183476
\(248\) −2.97856 −0.189139
\(249\) −8.10090 + 17.9858i −0.513374 + 1.13980i
\(250\) 3.30479i 0.209013i
\(251\) −2.17697 −0.137409 −0.0687047 0.997637i \(-0.521887\pi\)
−0.0687047 + 0.997637i \(0.521887\pi\)
\(252\) 5.59690 5.62803i 0.352571 0.354533i
\(253\) −0.616447 −0.0387557
\(254\) 1.27261i 0.0798509i
\(255\) −0.750862 + 1.66708i −0.0470208 + 0.104397i
\(256\) 1.00000 0.0625000
\(257\) 12.3872 0.772694 0.386347 0.922353i \(-0.373737\pi\)
0.386347 + 0.922353i \(0.373737\pi\)
\(258\) 17.9058 + 8.06487i 1.11477 + 0.502097i
\(259\) 0.351207 + 5.50108i 0.0218230 + 0.341821i
\(260\) 1.08261i 0.0671407i
\(261\) 4.81073 4.25706i 0.297777 0.263506i
\(262\) 3.12774i 0.193233i
\(263\) 15.9794i 0.985333i 0.870218 + 0.492666i \(0.163978\pi\)
−0.870218 + 0.492666i \(0.836022\pi\)
\(264\) 0.438482 0.973527i 0.0269867 0.0599165i
\(265\) 0.00307488i 0.000188888i
\(266\) −0.150058 2.35040i −0.00920062 0.144113i
\(267\) 11.1056 24.6570i 0.679653 1.50898i
\(268\) −5.51592 −0.336938
\(269\) 27.8643 1.69892 0.849459 0.527655i \(-0.176929\pi\)
0.849459 + 0.527655i \(0.176929\pi\)
\(270\) −0.515236 1.65842i −0.0313563 0.100929i
\(271\) 13.5793i 0.824883i −0.910984 0.412442i \(-0.864676\pi\)
0.910984 0.412442i \(-0.135324\pi\)
\(272\) 3.15851 0.191513
\(273\) −5.22140 + 13.8957i −0.316014 + 0.841006i
\(274\) −9.47914 −0.572656
\(275\) 3.01338i 0.181714i
\(276\) 1.57925 + 0.711304i 0.0950600 + 0.0428155i
\(277\) 27.2647 1.63817 0.819087 0.573669i \(-0.194480\pi\)
0.819087 + 0.573669i \(0.194480\pi\)
\(278\) −12.4667 −0.747700
\(279\) 6.69183 5.92166i 0.400629 0.354521i
\(280\) −0.882446 + 0.0563383i −0.0527362 + 0.00336685i
\(281\) 10.5377i 0.628626i 0.949319 + 0.314313i \(0.101774\pi\)
−0.949319 + 0.314313i \(0.898226\pi\)
\(282\) 4.67505 + 2.10567i 0.278395 + 0.125391i
\(283\) 15.1695i 0.901732i 0.892592 + 0.450866i \(0.148885\pi\)
−0.892592 + 0.450866i \(0.851115\pi\)
\(284\) 4.57347i 0.271386i
\(285\) −0.469842 0.211619i −0.0278310 0.0125352i
\(286\) 1.99685i 0.118076i
\(287\) −0.856764 13.4198i −0.0505732 0.792146i
\(288\) −2.24666 + 1.98809i −0.132386 + 0.117149i
\(289\) −7.02382 −0.413166
\(290\) −0.715642 −0.0420240
\(291\) −16.2183 7.30479i −0.950731 0.428214i
\(292\) 6.21012i 0.363420i
\(293\) −19.4813 −1.13811 −0.569055 0.822299i \(-0.692691\pi\)
−0.569055 + 0.822299i \(0.692691\pi\)
\(294\) 11.5982 + 3.53289i 0.676422 + 0.206042i
\(295\) −4.38657 −0.255396
\(296\) 2.08345i 0.121098i
\(297\) 0.950342 + 3.05893i 0.0551444 + 0.177497i
\(298\) −11.1915 −0.648303
\(299\) −3.23929 −0.187333
\(300\) 3.47707 7.71988i 0.200749 0.445707i
\(301\) 1.91127 + 29.9370i 0.110164 + 1.72554i
\(302\) 15.7569i 0.906710i
\(303\) 7.91878 17.5815i 0.454922 1.01003i
\(304\) 0.890178i 0.0510552i
\(305\) 2.98362i 0.170841i
\(306\) −7.09610 + 6.27941i −0.405657 + 0.358970i
\(307\) 11.1963i 0.639008i 0.947585 + 0.319504i \(0.103516\pi\)
−0.947585 + 0.319504i \(0.896484\pi\)
\(308\) 1.62765 0.103915i 0.0927441 0.00592109i
\(309\) 7.42900 + 3.34606i 0.422621 + 0.190351i
\(310\) −0.995473 −0.0565391
\(311\) 9.86492 0.559388 0.279694 0.960089i \(-0.409767\pi\)
0.279694 + 0.960089i \(0.409767\pi\)
\(312\) 2.30412 5.11567i 0.130445 0.289618i
\(313\) 16.5493i 0.935423i −0.883881 0.467711i \(-0.845079\pi\)
0.883881 0.467711i \(-0.154921\pi\)
\(314\) 0.132472 0.00747585
\(315\) 1.87055 1.88096i 0.105394 0.105980i
\(316\) 7.38606 0.415499
\(317\) 12.6369i 0.709758i 0.934912 + 0.354879i \(0.115478\pi\)
−0.934912 + 0.354879i \(0.884522\pi\)
\(318\) 0.00654428 0.0145298i 0.000366985 0.000814788i
\(319\) 1.31999 0.0739050
\(320\) 0.334212 0.0186830
\(321\) −10.5286 4.74215i −0.587651 0.264681i
\(322\) 0.168570 + 2.64038i 0.00939406 + 0.147142i
\(323\) 2.81164i 0.156444i
\(324\) 1.09498 8.93314i 0.0608322 0.496286i
\(325\) 15.8347i 0.878348i
\(326\) 1.56309i 0.0865714i
\(327\) 10.4634 23.2310i 0.578625 1.28468i
\(328\) 5.08253i 0.280636i
\(329\) 0.499017 + 7.81628i 0.0275117 + 0.430926i
\(330\) 0.146546 0.325365i 0.00806709 0.0179107i
\(331\) −19.5688 −1.07560 −0.537799 0.843073i \(-0.680744\pi\)
−0.537799 + 0.843073i \(0.680744\pi\)
\(332\) 11.3888 0.625042
\(333\) 4.14208 + 4.68080i 0.226985 + 0.256506i
\(334\) 9.97417i 0.545763i
\(335\) −1.84349 −0.100721
\(336\) −4.28973 1.61190i −0.234024 0.0879361i
\(337\) 19.1229 1.04169 0.520846 0.853651i \(-0.325617\pi\)
0.520846 + 0.853651i \(0.325617\pi\)
\(338\) 2.50697i 0.136361i
\(339\) 26.7169 + 12.0334i 1.45106 + 0.653567i
\(340\) 1.05561 0.0572486
\(341\) 1.83613 0.0994319
\(342\) −1.76976 1.99993i −0.0956974 0.108144i
\(343\) 3.52082 + 18.1825i 0.190106 + 0.981764i
\(344\) 11.3381i 0.611312i
\(345\) 0.527806 + 0.237727i 0.0284161 + 0.0127988i
\(346\) 12.3935i 0.666277i
\(347\) 13.6981i 0.735354i −0.929954 0.367677i \(-0.880153\pi\)
0.929954 0.367677i \(-0.119847\pi\)
\(348\) −3.38163 1.52310i −0.181274 0.0816469i
\(349\) 11.7210i 0.627412i −0.949520 0.313706i \(-0.898429\pi\)
0.949520 0.313706i \(-0.101571\pi\)
\(350\) 12.9070 0.824023i 0.689906 0.0440459i
\(351\) 4.99384 + 16.0740i 0.266551 + 0.857966i
\(352\) −0.616447 −0.0328567
\(353\) −8.43379 −0.448885 −0.224443 0.974487i \(-0.572056\pi\)
−0.224443 + 0.974487i \(0.572056\pi\)
\(354\) −20.7279 9.33594i −1.10167 0.496200i
\(355\) 1.52851i 0.0811249i
\(356\) −15.6130 −0.827490
\(357\) −13.5492 5.09119i −0.717097 0.269454i
\(358\) 4.94693 0.261453
\(359\) 22.4082i 1.18266i 0.806430 + 0.591330i \(0.201397\pi\)
−0.806430 + 0.591330i \(0.798603\pi\)
\(360\) −0.750862 + 0.664445i −0.0395739 + 0.0350193i
\(361\) 18.2076 0.958294
\(362\) −11.2427 −0.590902
\(363\) 7.55405 16.7717i 0.396485 0.880285i
\(364\) 8.55295 0.546049i 0.448297 0.0286207i
\(365\) 2.07550i 0.108637i
\(366\) −6.35003 + 14.0985i −0.331922 + 0.736940i
\(367\) 23.8207i 1.24343i −0.783244 0.621714i \(-0.786436\pi\)
0.783244 0.621714i \(-0.213564\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) −10.1045 11.4187i −0.526022 0.594435i
\(370\) 0.696313i 0.0361996i
\(371\) 0.0242925 0.00155091i 0.00126120 8.05193e-5i
\(372\) −4.70391 2.11867i −0.243887 0.109848i
\(373\) −36.8075 −1.90582 −0.952910 0.303254i \(-0.901927\pi\)
−0.952910 + 0.303254i \(0.901927\pi\)
\(374\) −1.94705 −0.100680
\(375\) 2.35071 5.21911i 0.121390 0.269514i
\(376\) 2.96029i 0.152665i
\(377\) 6.93624 0.357235
\(378\) 12.8422 4.90700i 0.660530 0.252389i
\(379\) 0.647490 0.0332593 0.0166297 0.999862i \(-0.494706\pi\)
0.0166297 + 0.999862i \(0.494706\pi\)
\(380\) 0.297508i 0.0152619i
\(381\) 0.905216 2.00978i 0.0463756 0.102964i
\(382\) −11.5303 −0.589942
\(383\) 23.8151 1.21689 0.608447 0.793595i \(-0.291793\pi\)
0.608447 + 0.793595i \(0.291793\pi\)
\(384\) 1.57925 + 0.711304i 0.0805910 + 0.0362986i
\(385\) 0.543981 0.0347296i 0.0277239 0.00176998i
\(386\) 5.65666i 0.287916i
\(387\) 22.5413 + 25.4730i 1.14584 + 1.29486i
\(388\) 10.2696i 0.521358i
\(389\) 33.3678i 1.69182i 0.533329 + 0.845908i \(0.320941\pi\)
−0.533329 + 0.845908i \(0.679059\pi\)
\(390\) 0.770067 1.70972i 0.0389938 0.0865750i
\(391\) 3.15851i 0.159733i
\(392\) −0.890178 6.94317i −0.0449608 0.350683i
\(393\) −2.22478 + 4.93950i −0.112225 + 0.249165i
\(394\) −3.68947 −0.185873
\(395\) 2.46851 0.124204
\(396\) 1.38495 1.22555i 0.0695963 0.0615864i
\(397\) 6.35096i 0.318745i 0.987218 + 0.159373i \(0.0509472\pi\)
−0.987218 + 0.159373i \(0.949053\pi\)
\(398\) −9.66592 −0.484509
\(399\) 1.43487 3.81862i 0.0718335 0.191170i
\(400\) −4.88830 −0.244415
\(401\) 30.0803i 1.50214i 0.660223 + 0.751069i \(0.270462\pi\)
−0.660223 + 0.751069i \(0.729538\pi\)
\(402\) −8.71104 3.92350i −0.434467 0.195686i
\(403\) 9.64845 0.480623
\(404\) −11.1328 −0.553875
\(405\) 0.365956 2.98557i 0.0181845 0.148354i
\(406\) −0.360956 5.65379i −0.0179140 0.280593i
\(407\) 1.28433i 0.0636621i
\(408\) 4.98809 + 2.24666i 0.246947 + 0.111226i
\(409\) 7.71976i 0.381718i 0.981617 + 0.190859i \(0.0611273\pi\)
−0.981617 + 0.190859i \(0.938873\pi\)
\(410\) 1.69864i 0.0838901i
\(411\) −14.9700 6.74255i −0.738415 0.332586i
\(412\) 4.70411i 0.231755i
\(413\) −2.21250 34.6552i −0.108870 1.70527i
\(414\) 1.98809 + 2.24666i 0.0977094 + 0.110417i
\(415\) 3.80628 0.186843
\(416\) −3.23929 −0.158819
\(417\) −19.6880 8.86759i −0.964127 0.434248i
\(418\) 0.548748i 0.0268401i
\(419\) −27.4462 −1.34083 −0.670417 0.741984i \(-0.733885\pi\)
−0.670417 + 0.741984i \(0.733885\pi\)
\(420\) −1.43368 0.538715i −0.0699565 0.0262866i
\(421\) −1.72287 −0.0839678 −0.0419839 0.999118i \(-0.513368\pi\)
−0.0419839 + 0.999118i \(0.513368\pi\)
\(422\) 9.28923i 0.452192i
\(423\) 5.88533 + 6.65077i 0.286155 + 0.323372i
\(424\) −0.00920039 −0.000446810
\(425\) −15.4398 −0.748938
\(426\) −3.25313 + 7.22268i −0.157615 + 0.349940i
\(427\) −23.5714 + 1.50488i −1.14070 + 0.0728262i
\(428\) 6.66683i 0.322254i
\(429\) −1.42037 + 3.15354i −0.0685762 + 0.152254i
\(430\) 3.78935i 0.182739i
\(431\) 28.3079i 1.36354i 0.731566 + 0.681771i \(0.238790\pi\)
−0.731566 + 0.681771i \(0.761210\pi\)
\(432\) −4.96219 + 1.54164i −0.238744 + 0.0741724i
\(433\) 3.77079i 0.181213i 0.995887 + 0.0906064i \(0.0288805\pi\)
−0.995887 + 0.0906064i \(0.971119\pi\)
\(434\) −0.502098 7.86453i −0.0241015 0.377510i
\(435\) −1.13018 0.509040i −0.0541881 0.0244066i
\(436\) −14.7101 −0.704486
\(437\) 0.890178 0.0425830
\(438\) −4.41729 + 9.80737i −0.211066 + 0.468614i
\(439\) 4.15471i 0.198293i −0.995073 0.0991467i \(-0.968389\pi\)
0.995073 0.0991467i \(-0.0316113\pi\)
\(440\) −0.206024 −0.00982182
\(441\) 15.8036 + 13.8292i 0.752552 + 0.658533i
\(442\) −10.2313 −0.486655
\(443\) 16.9438i 0.805025i 0.915414 + 0.402513i \(0.131863\pi\)
−0.915414 + 0.402513i \(0.868137\pi\)
\(444\) 1.48196 3.29029i 0.0703309 0.156150i
\(445\) −5.21807 −0.247360
\(446\) −26.0351 −1.23280
\(447\) −17.6742 7.96053i −0.835959 0.376520i
\(448\) 0.168570 + 2.64038i 0.00796420 + 0.124746i
\(449\) 19.5254i 0.921459i 0.887541 + 0.460730i \(0.152412\pi\)
−0.887541 + 0.460730i \(0.847588\pi\)
\(450\) 10.9824 9.71840i 0.517714 0.458130i
\(451\) 3.13311i 0.147533i
\(452\) 16.9174i 0.795729i
\(453\) 11.2080 24.8842i 0.526597 1.16916i
\(454\) 1.73870i 0.0816010i
\(455\) 2.85850 0.182496i 0.134009 0.00855555i
\(456\) −0.633187 + 1.40582i −0.0296517 + 0.0658334i
\(457\) −19.7471 −0.923729 −0.461864 0.886951i \(-0.652819\pi\)
−0.461864 + 0.886951i \(0.652819\pi\)
\(458\) −5.40527 −0.252572
\(459\) −15.6731 + 4.86930i −0.731559 + 0.227279i
\(460\) 0.334212i 0.0155827i
\(461\) 24.1439 1.12449 0.562247 0.826969i \(-0.309937\pi\)
0.562247 + 0.826969i \(0.309937\pi\)
\(462\) 2.64439 + 0.993648i 0.123028 + 0.0462287i
\(463\) −34.1392 −1.58658 −0.793292 0.608841i \(-0.791635\pi\)
−0.793292 + 0.608841i \(0.791635\pi\)
\(464\) 2.14128i 0.0994065i
\(465\) −1.57211 0.708084i −0.0729046 0.0328366i
\(466\) 13.3463 0.618255
\(467\) −17.3020 −0.800642 −0.400321 0.916375i \(-0.631101\pi\)
−0.400321 + 0.916375i \(0.631101\pi\)
\(468\) 7.27760 6.44002i 0.336407 0.297690i
\(469\) −0.929820 14.5641i −0.0429351 0.672508i
\(470\) 0.989366i 0.0456360i
\(471\) 0.209208 + 0.0942282i 0.00963978 + 0.00434181i
\(472\) 13.1251i 0.604132i
\(473\) 6.98937i 0.321371i
\(474\) 11.6645 + 5.25374i 0.535767 + 0.241312i
\(475\) 4.35146i 0.199659i
\(476\) 0.532431 + 8.33965i 0.0244039 + 0.382247i
\(477\) 0.0206702 0.0182912i 0.000946421 0.000837497i
\(478\) −29.0538 −1.32889
\(479\) 6.66557 0.304558 0.152279 0.988338i \(-0.451339\pi\)
0.152279 + 0.988338i \(0.451339\pi\)
\(480\) 0.527806 + 0.237727i 0.0240910 + 0.0108507i
\(481\) 6.74890i 0.307723i
\(482\) 16.1968 0.737744
\(483\) −1.61190 + 4.28973i −0.0733438 + 0.195190i
\(484\) −10.6200 −0.482727
\(485\) 3.43221i 0.155849i
\(486\) 8.08343 13.3288i 0.366672 0.604609i
\(487\) 16.2562 0.736637 0.368319 0.929700i \(-0.379934\pi\)
0.368319 + 0.929700i \(0.379934\pi\)
\(488\) 8.92731 0.404120
\(489\) −1.11183 + 2.46851i −0.0502787 + 0.111630i
\(490\) −0.297508 2.32049i −0.0134401 0.104829i
\(491\) 24.7150i 1.11537i −0.830051 0.557687i \(-0.811689\pi\)
0.830051 0.557687i \(-0.188311\pi\)
\(492\) −3.61523 + 8.02661i −0.162987 + 0.361868i
\(493\) 6.76326i 0.304602i
\(494\) 2.88355i 0.129737i
\(495\) 0.462867 0.409595i 0.0208043 0.0184099i
\(496\) 2.97856i 0.133742i
\(497\) −12.0757 + 0.770951i −0.541668 + 0.0345819i
\(498\) 17.9858 + 8.10090i 0.805964 + 0.363010i
\(499\) 14.1996 0.635662 0.317831 0.948147i \(-0.397045\pi\)
0.317831 + 0.948147i \(0.397045\pi\)
\(500\) −3.30479 −0.147795
\(501\) −7.09467 + 15.7518i −0.316967 + 0.703737i
\(502\) 2.17697i 0.0971631i
\(503\) 3.22976 0.144008 0.0720038 0.997404i \(-0.477061\pi\)
0.0720038 + 0.997404i \(0.477061\pi\)
\(504\) −5.62803 5.59690i −0.250692 0.249306i
\(505\) −3.72070 −0.165569
\(506\) 0.616447i 0.0274044i
\(507\) 1.78322 3.95915i 0.0791955 0.175832i
\(508\) −1.27261 −0.0564631
\(509\) 34.5726 1.53240 0.766202 0.642600i \(-0.222144\pi\)
0.766202 + 0.642600i \(0.222144\pi\)
\(510\) 1.66708 + 0.750862i 0.0738196 + 0.0332487i
\(511\) −16.3971 + 1.04684i −0.725363 + 0.0463096i
\(512\) 1.00000i 0.0441942i
\(513\) −1.37234 4.41723i −0.0605902 0.195026i
\(514\) 12.3872i 0.546377i
\(515\) 1.57217i 0.0692782i
\(516\) 8.06487 17.9058i 0.355036 0.788260i
\(517\) 1.82486i 0.0802574i
\(518\) 5.50108 0.351207i 0.241704 0.0154312i
\(519\) −8.81553 + 19.5725i −0.386959 + 0.859136i
\(520\) −1.08261 −0.0474757
\(521\) −19.4594 −0.852530 −0.426265 0.904598i \(-0.640171\pi\)
−0.426265 + 0.904598i \(0.640171\pi\)
\(522\) −4.25706 4.81073i −0.186327 0.210560i
\(523\) 0.456621i 0.0199667i −0.999950 0.00998333i \(-0.996822\pi\)
0.999950 0.00998333i \(-0.00317784\pi\)
\(524\) 3.12774 0.136636
\(525\) 20.9695 + 7.87943i 0.915184 + 0.343887i
\(526\) 15.9794 0.696735
\(527\) 9.40783i 0.409811i
\(528\) −0.973527 0.438482i −0.0423673 0.0190825i
\(529\) −1.00000 −0.0434783
\(530\) −0.00307488 −0.000133564
\(531\) −26.0939 29.4877i −1.13238 1.27966i
\(532\) −2.35040 + 0.150058i −0.101903 + 0.00650582i
\(533\) 16.4638i 0.713127i
\(534\) −24.6570 11.1056i −1.06701 0.480588i
\(535\) 2.22814i 0.0963308i
\(536\) 5.51592i 0.238251i
\(537\) 7.81246 + 3.51877i 0.337132 + 0.151846i
\(538\) 27.8643i 1.20132i
\(539\) 0.548748 + 4.28010i 0.0236362 + 0.184357i
\(540\) −1.65842 + 0.515236i −0.0713672 + 0.0221722i
\(541\) −36.4914 −1.56889 −0.784445 0.620199i \(-0.787052\pi\)
−0.784445 + 0.620199i \(0.787052\pi\)
\(542\) −13.5793 −0.583281
\(543\) −17.7550 7.99696i −0.761942 0.343182i
\(544\) 3.15851i 0.135420i
\(545\) −4.91629 −0.210591
\(546\) 13.8957 + 5.22140i 0.594681 + 0.223455i
\(547\) 21.9239 0.937398 0.468699 0.883358i \(-0.344723\pi\)
0.468699 + 0.883358i \(0.344723\pi\)
\(548\) 9.47914i 0.404929i
\(549\) −20.0566 + 17.7483i −0.855997 + 0.757479i
\(550\) 3.01338 0.128491
\(551\) −1.90612 −0.0812035
\(552\) 0.711304 1.57925i 0.0302751 0.0672176i
\(553\) 1.24507 + 19.5020i 0.0529458 + 0.829309i
\(554\) 27.2647i 1.15836i
\(555\) 0.495291 1.09966i 0.0210239 0.0466778i
\(556\) 12.4667i 0.528704i
\(557\) 18.2808i 0.774583i −0.921957 0.387292i \(-0.873411\pi\)
0.921957 0.387292i \(-0.126589\pi\)
\(558\) −5.92166 6.69183i −0.250684 0.283288i
\(559\) 36.7276i 1.55341i
\(560\) 0.0563383 + 0.882446i 0.00238073 + 0.0372901i
\(561\) −3.07489 1.38495i −0.129822 0.0584726i
\(562\) 10.5377 0.444505
\(563\) −15.4798 −0.652397 −0.326198 0.945301i \(-0.605768\pi\)
−0.326198 + 0.945301i \(0.605768\pi\)
\(564\) 2.10567 4.67505i 0.0886646 0.196855i
\(565\) 5.65401i 0.237866i
\(566\) 15.1695 0.637621
\(567\) 23.7714 + 1.38529i 0.998306 + 0.0581769i
\(568\) 4.57347 0.191899
\(569\) 41.5182i 1.74053i 0.492579 + 0.870267i \(0.336054\pi\)
−0.492579 + 0.870267i \(0.663946\pi\)
\(570\) −0.211619 + 0.469842i −0.00886374 + 0.0196795i
\(571\) −5.38690 −0.225435 −0.112717 0.993627i \(-0.535955\pi\)
−0.112717 + 0.993627i \(0.535955\pi\)
\(572\) 1.99685 0.0834927
\(573\) −18.2093 8.20156i −0.760705 0.342625i
\(574\) −13.4198 + 0.856764i −0.560131 + 0.0357606i
\(575\) 4.88830i 0.203856i
\(576\) 1.98809 + 2.24666i 0.0828372 + 0.0936109i
\(577\) 32.6637i 1.35981i 0.733301 + 0.679905i \(0.237979\pi\)
−0.733301 + 0.679905i \(0.762021\pi\)
\(578\) 7.02382i 0.292152i
\(579\) −4.02361 + 8.93330i −0.167215 + 0.371255i
\(580\) 0.715642i 0.0297154i
\(581\) 1.91981 + 30.0707i 0.0796473 + 1.24754i
\(582\) −7.30479 + 16.2183i −0.302793 + 0.672269i
\(583\) 0.00567155 0.000234892
\(584\) 6.21012 0.256977
\(585\) 2.43226 2.15233i 0.100562 0.0889880i
\(586\) 19.4813i 0.804766i
\(587\) −28.9317 −1.19414 −0.597070 0.802189i \(-0.703668\pi\)
−0.597070 + 0.802189i \(0.703668\pi\)
\(588\) 3.53289 11.5982i 0.145694 0.478303i
\(589\) −2.65145 −0.109251
\(590\) 4.38657i 0.180592i
\(591\) −5.82662 2.62434i −0.239675 0.107951i
\(592\) −2.08345 −0.0856291
\(593\) −4.62778 −0.190040 −0.0950200 0.995475i \(-0.530292\pi\)
−0.0950200 + 0.995475i \(0.530292\pi\)
\(594\) 3.05893 0.950342i 0.125509 0.0389930i
\(595\) 0.177945 + 2.78721i 0.00729503 + 0.114265i
\(596\) 11.1915i 0.458420i
\(597\) −15.2649 6.87541i −0.624753 0.281392i
\(598\) 3.23929i 0.132465i
\(599\) 23.0851i 0.943230i −0.881804 0.471615i \(-0.843671\pi\)
0.881804 0.471615i \(-0.156329\pi\)
\(600\) −7.71988 3.47707i −0.315163 0.141951i
\(601\) 18.8377i 0.768405i −0.923249 0.384203i \(-0.874476\pi\)
0.923249 0.384203i \(-0.125524\pi\)
\(602\) 29.9370 1.91127i 1.22014 0.0778977i
\(603\) −10.9662 12.3924i −0.446576 0.504658i
\(604\) −15.7569 −0.641141
\(605\) −3.54933 −0.144301
\(606\) −17.5815 7.91878i −0.714198 0.321678i
\(607\) 2.17865i 0.0884286i −0.999022 0.0442143i \(-0.985922\pi\)
0.999022 0.0442143i \(-0.0140784\pi\)
\(608\) 0.890178 0.0361015
\(609\) 3.45152 9.18552i 0.139863 0.372216i
\(610\) 2.98362 0.120803
\(611\) 9.58925i 0.387940i
\(612\) 6.27941 + 7.09610i 0.253830 + 0.286843i
\(613\) −18.6916 −0.754947 −0.377473 0.926020i \(-0.623207\pi\)
−0.377473 + 0.926020i \(0.623207\pi\)
\(614\) 11.1963 0.451847
\(615\) −1.20825 + 2.68259i −0.0487215 + 0.108173i
\(616\) −0.103915 1.62765i −0.00418684 0.0655800i
\(617\) 43.5422i 1.75294i 0.481454 + 0.876471i \(0.340109\pi\)
−0.481454 + 0.876471i \(0.659891\pi\)
\(618\) 3.34606 7.42900i 0.134598 0.298838i
\(619\) 1.99564i 0.0802115i 0.999195 + 0.0401057i \(0.0127695\pi\)
−0.999195 + 0.0401057i \(0.987231\pi\)
\(620\) 0.995473i 0.0399792i
\(621\) 1.54164 + 4.96219i 0.0618640 + 0.199126i
\(622\) 9.86492i 0.395547i
\(623\) −2.63190 41.2243i −0.105445 1.65162i
\(624\) −5.11567 2.30412i −0.204791 0.0922388i
\(625\) 23.3370 0.933480
\(626\) −16.5493 −0.661444
\(627\) 0.390327 0.866612i 0.0155881 0.0346092i
\(628\) 0.132472i 0.00528622i
\(629\) −6.58059 −0.262385
\(630\) −1.88096 1.87055i −0.0749391 0.0745246i
\(631\) 24.2580 0.965696 0.482848 0.875704i \(-0.339602\pi\)
0.482848 + 0.875704i \(0.339602\pi\)
\(632\) 7.38606i 0.293802i
\(633\) 6.60747 14.6701i 0.262623 0.583082i
\(634\) 12.6369 0.501874
\(635\) −0.425323 −0.0168784
\(636\) −0.0145298 0.00654428i −0.000576142 0.000259497i
\(637\) 2.88355 + 22.4910i 0.114250 + 0.891125i
\(638\) 1.31999i 0.0522588i
\(639\) −10.2750 + 9.09248i −0.406474 + 0.359693i
\(640\) 0.334212i 0.0132109i
\(641\) 26.6761i 1.05364i 0.849976 + 0.526821i \(0.176616\pi\)
−0.849976 + 0.526821i \(0.823384\pi\)
\(642\) −4.74215 + 10.5286i −0.187158 + 0.415532i
\(643\) 48.6820i 1.91983i 0.280288 + 0.959916i \(0.409570\pi\)
−0.280288 + 0.959916i \(0.590430\pi\)
\(644\) 2.64038 0.168570i 0.104045 0.00664260i
\(645\) 2.69538 5.98435i 0.106130 0.235633i
\(646\) 2.81164 0.110622
\(647\) 10.9109 0.428953 0.214477 0.976729i \(-0.431195\pi\)
0.214477 + 0.976729i \(0.431195\pi\)
\(648\) −8.93314 1.09498i −0.350927 0.0430149i
\(649\) 8.09093i 0.317597i
\(650\) 15.8347 0.621086
\(651\) 4.80114 12.7772i 0.188171 0.500780i
\(652\) 1.56309 0.0612152
\(653\) 28.1573i 1.10188i −0.834545 0.550940i \(-0.814269\pi\)
0.834545 0.550940i \(-0.185731\pi\)
\(654\) −23.2310 10.4634i −0.908404 0.409150i
\(655\) 1.04533 0.0408444
\(656\) 5.08253 0.198440
\(657\) −13.9520 + 12.3463i −0.544321 + 0.481675i
\(658\) 7.81628 0.499017i 0.304710 0.0194537i
\(659\) 8.33441i 0.324663i 0.986736 + 0.162331i \(0.0519013\pi\)
−0.986736 + 0.162331i \(0.948099\pi\)
\(660\) −0.325365 0.146546i −0.0126648 0.00570429i
\(661\) 10.3792i 0.403705i 0.979416 + 0.201853i \(0.0646962\pi\)
−0.979416 + 0.201853i \(0.935304\pi\)
\(662\) 19.5688i 0.760562i
\(663\) −16.1579 7.27760i −0.627521 0.282639i
\(664\) 11.3888i 0.441971i
\(665\) −0.785534 + 0.0501511i −0.0304617 + 0.00194478i
\(666\) 4.68080 4.14208i 0.181377 0.160502i
\(667\) 2.14128 0.0829107
\(668\) 9.97417 0.385912
\(669\) −41.1161 18.5189i −1.58964 0.715981i
\(670\) 1.84349i 0.0712202i
\(671\) −5.50321 −0.212449
\(672\) −1.61190 + 4.28973i −0.0621802 + 0.165480i
\(673\) 37.1417 1.43171 0.715854 0.698250i \(-0.246038\pi\)
0.715854 + 0.698250i \(0.246038\pi\)
\(674\) 19.1229i 0.736587i
\(675\) 24.2567 7.53602i 0.933640 0.290062i
\(676\) −2.50697 −0.0964219
\(677\) 51.1129 1.96443 0.982215 0.187762i \(-0.0601233\pi\)
0.982215 + 0.187762i \(0.0601233\pi\)
\(678\) 12.0334 26.7169i 0.462141 1.02606i
\(679\) −27.1155 + 1.73114i −1.04060 + 0.0664352i
\(680\) 1.05561i 0.0404809i
\(681\) 1.23674 2.74584i 0.0473921 0.105221i
\(682\) 1.83613i 0.0703090i
\(683\) 9.54141i 0.365092i −0.983197 0.182546i \(-0.941566\pi\)
0.983197 0.182546i \(-0.0584338\pi\)
\(684\) −1.99993 + 1.76976i −0.0764692 + 0.0676683i
\(685\) 3.16804i 0.121045i
\(686\) 18.1825 3.52082i 0.694212 0.134425i
\(687\) −8.53630 3.84479i −0.325680 0.146688i
\(688\) −11.3381 −0.432263
\(689\) 0.0298028 0.00113539
\(690\) 0.237727 0.527806i 0.00905010 0.0200932i
\(691\) 9.55799i 0.363603i 0.983335 + 0.181802i \(0.0581929\pi\)
−0.983335 + 0.181802i \(0.941807\pi\)
\(692\) 12.3935 0.471129
\(693\) 3.46938 + 3.45019i 0.131791 + 0.131062i
\(694\) −13.6981 −0.519974
\(695\) 4.16651i 0.158045i
\(696\) −1.52310 + 3.38163i −0.0577330 + 0.128180i
\(697\) 16.0532 0.608059
\(698\) −11.7210 −0.443647
\(699\) 21.0772 + 9.49328i 0.797213 + 0.359069i
\(700\) −0.824023 12.9070i −0.0311451 0.487837i
\(701\) 28.0103i 1.05793i −0.848642 0.528967i \(-0.822579\pi\)
0.848642 0.528967i \(-0.177421\pi\)
\(702\) 16.0740 4.99384i 0.606674 0.188480i
\(703\) 1.85464i 0.0699490i
\(704\) 0.616447i 0.0232332i
\(705\) 0.703740 1.56246i 0.0265044 0.0588457i
\(706\) 8.43379i 0.317410i
\(707\) −1.87665 29.3947i −0.0705788 1.10550i
\(708\) −9.33594 + 20.7279i −0.350866 + 0.779002i
\(709\) 15.2373 0.572248 0.286124 0.958193i \(-0.407633\pi\)
0.286124 + 0.958193i \(0.407633\pi\)
\(710\) 1.52851 0.0573640
\(711\) 14.6842 + 16.5940i 0.550700 + 0.622323i
\(712\) 15.6130i 0.585124i
\(713\) 2.97856 0.111548
\(714\) −5.09119 + 13.5492i −0.190533 + 0.507064i
\(715\) 0.667373 0.0249583
\(716\) 4.94693i 0.184875i
\(717\) −45.8833 20.6661i −1.71354 0.771789i
\(718\) 22.4082 0.836267
\(719\) 44.6979 1.66695 0.833475 0.552558i \(-0.186348\pi\)
0.833475 + 0.552558i \(0.186348\pi\)
\(720\) 0.664445 + 0.750862i 0.0247624 + 0.0279830i
\(721\) 12.4206 0.792974i 0.462568 0.0295319i
\(722\) 18.2076i 0.677616i
\(723\) 25.5789 + 11.5208i 0.951288 + 0.428465i
\(724\) 11.2427i 0.417831i
\(725\) 10.4672i 0.388743i
\(726\) −16.7717 7.55405i −0.622455 0.280357i
\(727\) 24.8349i 0.921074i −0.887640 0.460537i \(-0.847657\pi\)
0.887640 0.460537i \(-0.152343\pi\)
\(728\) −0.546049 8.55295i −0.0202379 0.316994i
\(729\) 22.2467 15.2999i 0.823951 0.566661i
\(730\) 2.07550 0.0768177
\(731\) −35.8116 −1.32454
\(732\) 14.0985 + 6.35003i 0.521095 + 0.234704i
\(733\) 4.68413i 0.173012i 0.996251 + 0.0865061i \(0.0275702\pi\)
−0.996251 + 0.0865061i \(0.972430\pi\)
\(734\) −23.8207 −0.879237
\(735\) 1.18073 3.87627i 0.0435520 0.142978i
\(736\) −1.00000 −0.0368605
\(737\) 3.40027i 0.125251i
\(738\) −11.4187 + 10.1045i −0.420329 + 0.371953i
\(739\) −35.0108 −1.28789 −0.643946 0.765071i \(-0.722704\pi\)
−0.643946 + 0.765071i \(0.722704\pi\)
\(740\) −0.696313 −0.0255970
\(741\) 2.05108 4.55386i 0.0753483 0.167290i
\(742\) −0.00155091 0.0242925i −5.69358e−5 0.000891805i
\(743\) 1.09183i 0.0400553i −0.999799 0.0200276i \(-0.993625\pi\)
0.999799 0.0200276i \(-0.00637542\pi\)
\(744\) −2.11867 + 4.70391i −0.0776741 + 0.172454i
\(745\) 3.74032i 0.137035i
\(746\) 36.8075i 1.34762i
\(747\) 22.6420 + 25.5868i 0.828427 + 0.936171i
\(748\) 1.94705i 0.0711914i
\(749\) −17.6029 + 1.12383i −0.643198 + 0.0410639i
\(750\) −5.21911 2.35071i −0.190575 0.0858359i
\(751\) −17.0491 −0.622130 −0.311065 0.950389i \(-0.600686\pi\)
−0.311065 + 0.950389i \(0.600686\pi\)
\(752\) −2.96029 −0.107951
\(753\) −1.54849 + 3.43800i −0.0564301 + 0.125288i
\(754\) 6.93624i 0.252603i
\(755\) −5.26616 −0.191655
\(756\) −4.90700 12.8422i −0.178466 0.467065i
\(757\) 10.1936 0.370494 0.185247 0.982692i \(-0.440691\pi\)
0.185247 + 0.982692i \(0.440691\pi\)
\(758\) 0.647490i 0.0235179i
\(759\) −0.438482 + 0.973527i −0.0159159 + 0.0353368i
\(760\) 0.297508 0.0107918
\(761\) 53.5953 1.94283 0.971414 0.237393i \(-0.0762928\pi\)
0.971414 + 0.237393i \(0.0762928\pi\)
\(762\) −2.00978 0.905216i −0.0728067 0.0327925i
\(763\) −2.47969 38.8402i −0.0897706 1.40611i
\(764\) 11.5303i 0.417152i
\(765\) 2.09866 + 2.37160i 0.0758770 + 0.0857456i
\(766\) 23.8151i 0.860474i
\(767\) 42.5161i 1.53517i
\(768\) 0.711304 1.57925i 0.0256670 0.0569865i
\(769\) 38.8414i 1.40066i 0.713821 + 0.700328i \(0.246963\pi\)
−0.713821 + 0.700328i \(0.753037\pi\)
\(770\) −0.0347296 0.543981i −0.00125157 0.0196037i
\(771\) 8.81109 19.5626i 0.317324 0.704530i
\(772\) 5.65666 0.203588
\(773\) −15.9469 −0.573570 −0.286785 0.957995i \(-0.592586\pi\)
−0.286785 + 0.957995i \(0.592586\pi\)
\(774\) 25.4730 22.5413i 0.915607 0.810230i
\(775\) 14.5601i 0.523015i
\(776\) 10.2696 0.368656
\(777\) 8.93743 + 3.35830i 0.320628 + 0.120478i
\(778\) 33.3678 1.19629
\(779\) 4.52436i 0.162102i
\(780\) −1.70972 0.770067i −0.0612178 0.0275728i
\(781\) −2.81930 −0.100883
\(782\) −3.15851 −0.112948
\(783\) −3.30109 10.6254i −0.117971 0.379722i
\(784\) −6.94317 + 0.890178i −0.247970 + 0.0317921i
\(785\) 0.0442739i 0.00158020i
\(786\) 4.93950 + 2.22478i 0.176186 + 0.0793552i
\(787\) 1.53740i 0.0548025i −0.999625 0.0274012i \(-0.991277\pi\)
0.999625 0.0274012i \(-0.00872318\pi\)
\(788\) 3.68947i 0.131432i
\(789\) 25.2356 + 11.3662i 0.898410 + 0.404648i
\(790\) 2.46851i 0.0878258i
\(791\) 44.6684 2.85178i 1.58822 0.101397i
\(792\) −1.22555 1.38495i −0.0435482 0.0492120i
\(793\) −28.9182 −1.02691
\(794\) 6.35096 0.225387
\(795\) −0.00485602 0.00218718i −0.000172225 7.75712e-5i
\(796\) 9.66592i 0.342599i
\(797\) 27.4564 0.972554 0.486277 0.873805i \(-0.338355\pi\)
0.486277 + 0.873805i \(0.338355\pi\)
\(798\) −3.81862 1.43487i −0.135178 0.0507940i
\(799\) −9.35011 −0.330783
\(800\) 4.88830i 0.172828i
\(801\) −31.0402 35.0772i −1.09675 1.23939i
\(802\) 30.0803 1.06217
\(803\) −3.82821 −0.135095
\(804\) −3.92350 + 8.71104i −0.138371 + 0.307215i
\(805\) 0.882446 0.0563383i 0.0311021 0.00198566i
\(806\) 9.64845i 0.339852i
\(807\) 19.8200 44.0049i 0.697697 1.54904i
\(808\) 11.1328i 0.391649i
\(809\) 26.8772i 0.944952i −0.881344 0.472476i \(-0.843360\pi\)
0.881344 0.472476i \(-0.156640\pi\)
\(810\) −2.98557 0.365956i −0.104902 0.0128584i
\(811\) 25.2349i 0.886118i 0.896492 + 0.443059i \(0.146107\pi\)
−0.896492 + 0.443059i \(0.853893\pi\)
\(812\) −5.65379 + 0.360956i −0.198409 + 0.0126671i
\(813\) −21.4452 9.65901i −0.752115 0.338756i
\(814\) 1.28433 0.0450159
\(815\) 0.522403 0.0182990
\(816\) 2.24666 4.98809i 0.0786489 0.174618i
\(817\) 10.0930i 0.353108i
\(818\) 7.71976 0.269915
\(819\) 18.2308 + 18.1300i 0.637037 + 0.633514i
\(820\) 1.69864 0.0593192
\(821\) 48.8711i 1.70561i −0.522228 0.852806i \(-0.674899\pi\)
0.522228 0.852806i \(-0.325101\pi\)
\(822\) −6.74255 + 14.9700i −0.235174 + 0.522138i
\(823\) 23.4785 0.818411 0.409205 0.912442i \(-0.365806\pi\)
0.409205 + 0.912442i \(0.365806\pi\)
\(824\) −4.70411 −0.163876
\(825\) 4.75889 + 2.14343i 0.165683 + 0.0746247i
\(826\) −34.6552 + 2.21250i −1.20581 + 0.0769828i
\(827\) 14.5382i 0.505544i −0.967526 0.252772i \(-0.918658\pi\)
0.967526 0.252772i \(-0.0813422\pi\)
\(828\) 2.24666 1.98809i 0.0780769 0.0690910i
\(829\) 21.8284i 0.758131i 0.925370 + 0.379066i \(0.123755\pi\)
−0.925370 + 0.379066i \(0.876245\pi\)
\(830\) 3.80628i 0.132118i
\(831\) 19.3935 43.0578i 0.672752 1.49366i
\(832\) 3.23929i 0.112302i
\(833\) −21.9301 + 2.81164i −0.759832 + 0.0974174i
\(834\) −8.86759 + 19.6880i −0.307059 + 0.681741i
\(835\) 3.33349 0.115360
\(836\) −0.548748 −0.0189788
\(837\) −4.59189 14.7802i −0.158719 0.510879i
\(838\) 27.4462i 0.948113i
\(839\) −26.6696 −0.920737 −0.460368 0.887728i \(-0.652283\pi\)
−0.460368 + 0.887728i \(0.652283\pi\)
\(840\) −0.538715 + 1.43368i −0.0185874 + 0.0494667i
\(841\) 24.4149 0.841894
\(842\) 1.72287i 0.0593742i
\(843\) 16.6417 + 7.49550i 0.573170 + 0.258159i
\(844\) −9.28923 −0.319748
\(845\) −0.837860 −0.0288233
\(846\) 6.65077 5.88533i 0.228658 0.202342i
\(847\) −1.79022 28.0408i −0.0615125 0.963492i
\(848\) 0.00920039i 0.000315943i
\(849\) 23.9565 + 10.7901i 0.822184 + 0.370316i
\(850\) 15.4398i 0.529579i
\(851\) 2.08345i 0.0714196i
\(852\) 7.22268 + 3.25313i 0.247445 + 0.111450i
\(853\) 3.50989i 0.120176i 0.998193 + 0.0600882i \(0.0191382\pi\)
−0.998193 + 0.0600882i \(0.980862\pi\)
\(854\) 1.50488 + 23.5714i 0.0514959 + 0.806598i
\(855\) −0.668401 + 0.591474i −0.0228588 + 0.0202280i
\(856\) 6.66683 0.227868
\(857\) 32.7365 1.11826 0.559129 0.829080i \(-0.311135\pi\)
0.559129 + 0.829080i \(0.311135\pi\)
\(858\) 3.15354 + 1.42037i 0.107660 + 0.0484907i
\(859\) 18.9860i 0.647794i 0.946092 + 0.323897i \(0.104993\pi\)
−0.946092 + 0.323897i \(0.895007\pi\)
\(860\) −3.78935 −0.129216
\(861\) −21.8027 8.19251i −0.743034 0.279200i
\(862\) 28.3079 0.964170
\(863\) 22.9285i 0.780494i −0.920710 0.390247i \(-0.872390\pi\)
0.920710 0.390247i \(-0.127610\pi\)
\(864\) 1.54164 + 4.96219i 0.0524478 + 0.168817i
\(865\) 4.14205 0.140834
\(866\) 3.77079 0.128137
\(867\) −4.99607 + 11.0924i −0.169675 + 0.376718i
\(868\) −7.86453 + 0.502098i −0.266940 + 0.0170423i
\(869\) 4.55312i 0.154454i
\(870\) −0.509040 + 1.13018i −0.0172581 + 0.0383167i
\(871\) 17.8677i 0.605424i
\(872\) 14.7101i 0.498147i
\(873\) −23.0722 + 20.4168i −0.780877 + 0.691005i
\(874\) 0.890178i 0.0301107i
\(875\) −0.557090 8.72589i −0.0188331 0.294989i
\(876\) 9.80737 + 4.41729i 0.331360 + 0.149246i
\(877\) 32.0494 1.08223 0.541116 0.840948i \(-0.318002\pi\)
0.541116 + 0.840948i \(0.318002\pi\)
\(878\) −4.15471 −0.140215
\(879\) −13.8571 + 30.7660i −0.467390 + 1.03771i
\(880\) 0.206024i 0.00694507i
\(881\) 20.8969 0.704034 0.352017 0.935994i \(-0.385496\pi\)
0.352017 + 0.935994i \(0.385496\pi\)
\(882\) 13.8292 15.8036i 0.465653 0.532134i
\(883\) −51.9603 −1.74860 −0.874302 0.485383i \(-0.838680\pi\)
−0.874302 + 0.485383i \(0.838680\pi\)
\(884\) 10.2313i 0.344117i
\(885\) −3.12019 + 6.92751i −0.104884 + 0.232866i
\(886\) 16.9438 0.569239
\(887\) 13.1666 0.442091 0.221046 0.975263i \(-0.429053\pi\)
0.221046 + 0.975263i \(0.429053\pi\)
\(888\) −3.29029 1.48196i −0.110415 0.0497315i
\(889\) −0.214525 3.36018i −0.00719494 0.112697i
\(890\) 5.21807i 0.174910i
\(891\) 5.50681 + 0.674997i 0.184485 + 0.0226132i
\(892\) 26.0351i 0.871720i
\(893\) 2.63519i 0.0881831i
\(894\) −7.96053 + 17.6742i −0.266240 + 0.591112i
\(895\) 1.65332i 0.0552645i
\(896\) 2.64038 0.168570i 0.0882088 0.00563154i
\(897\) −2.30412 + 5.11567i −0.0769325 + 0.170807i
\(898\) 19.5254 0.651570
\(899\) −6.37794 −0.212716
\(900\) −9.71840 10.9824i −0.323947 0.366079i
\(901\) 0.0290595i 0.000968113i
\(902\) −3.13311 −0.104321
\(903\) 48.6376 + 18.2759i 1.61856 + 0.608184i
\(904\) −16.9174 −0.562665
\(905\) 3.75744i 0.124901i
\(906\) −24.8842 11.2080i −0.826723 0.372360i
\(907\) 3.89982 0.129491 0.0647457 0.997902i \(-0.479376\pi\)
0.0647457 + 0.997902i \(0.479376\pi\)
\(908\) −1.73870 −0.0577006
\(909\) −22.1329 25.0115i −0.734103 0.829580i
\(910\) −0.182496 2.85850i −0.00604969 0.0947584i
\(911\) 12.1667i 0.403102i 0.979478 + 0.201551i \(0.0645982\pi\)
−0.979478 + 0.201551i \(0.935402\pi\)
\(912\) 1.40582 + 0.633187i 0.0465513 + 0.0209669i
\(913\) 7.02059i 0.232348i
\(914\) 19.7471i 0.653175i
\(915\) 4.71189 + 2.12226i 0.155770 + 0.0701597i
\(916\) 5.40527i 0.178595i
\(917\) 0.527244 + 8.25841i 0.0174111 + 0.272717i
\(918\) 4.86930 + 15.6731i 0.160711 + 0.517290i
\(919\) −30.9169 −1.01985 −0.509927 0.860217i \(-0.670328\pi\)
−0.509927 + 0.860217i \(0.670328\pi\)
\(920\) −0.334212 −0.0110187
\(921\) 17.6818 + 7.96399i 0.582637 + 0.262422i
\(922\) 24.1439i 0.795137i
\(923\) −14.8148 −0.487636
\(924\) 0.993648 2.64439i 0.0326886 0.0869941i
\(925\) 10.1845 0.334865
\(926\) 34.1392i 1.12188i
\(927\) 10.5686 9.35221i 0.347117 0.307167i
\(928\) 2.14128 0.0702910
\(929\) −9.49474 −0.311512 −0.155756 0.987796i \(-0.549781\pi\)
−0.155756 + 0.987796i \(0.549781\pi\)
\(930\) −0.708084 + 1.57211i −0.0232190 + 0.0515514i
\(931\) −0.792417 6.18065i −0.0259704 0.202563i
\(932\) 13.3463i 0.437173i
\(933\) 7.01696 15.5792i 0.229725 0.510041i
\(934\) 17.3020i 0.566139i
\(935\) 0.650729i 0.0212811i
\(936\) −6.44002 7.27760i −0.210499 0.237876i
\(937\) 21.2783i 0.695132i −0.937655 0.347566i \(-0.887008\pi\)
0.937655 0.347566i \(-0.112992\pi\)
\(938\) −14.5641 + 0.929820i −0.475535 + 0.0303597i
\(939\) −26.1356 11.7716i −0.852903 0.384152i
\(940\) −0.989366 −0.0322695
\(941\) −11.8428 −0.386063 −0.193032 0.981193i \(-0.561832\pi\)
−0.193032 + 0.981193i \(0.561832\pi\)
\(942\) 0.0942282 0.209208i 0.00307012 0.00681635i
\(943\) 5.08253i 0.165510i
\(944\) 13.1251 0.427186
\(945\) −1.63998 4.29201i −0.0533485 0.139619i
\(946\) 6.98937 0.227244
\(947\) 36.6641i 1.19142i −0.803198 0.595712i \(-0.796870\pi\)
0.803198 0.595712i \(-0.203130\pi\)
\(948\) 5.25374 11.6645i 0.170634 0.378845i
\(949\) −20.1164 −0.653007
\(950\) −4.35146 −0.141180
\(951\) 19.9568 + 8.98866i 0.647145 + 0.291477i
\(952\) 8.33965 0.532431i 0.270290 0.0172562i
\(953\) 8.27408i 0.268024i 0.990980 + 0.134012i \(0.0427860\pi\)
−0.990980 + 0.134012i \(0.957214\pi\)
\(954\) −0.0182912 0.0206702i −0.000592200 0.000669221i
\(955\) 3.85357i 0.124699i
\(956\) 29.0538i 0.939666i
\(957\) 0.938912 2.08459i 0.0303507 0.0673854i
\(958\) 6.66557i 0.215355i
\(959\) −25.0285 + 1.59790i −0.808212 + 0.0515989i
\(960\) 0.237727 0.527806i 0.00767259 0.0170349i
\(961\) 22.1282 0.713811
\(962\) 6.74890 0.217593
\(963\) −14.9781 + 13.2543i −0.482663 + 0.427113i
\(964\) 16.1968i 0.521664i
\(965\) 1.89052 0.0608581
\(966\) 4.28973 + 1.61190i 0.138020 + 0.0518619i
\(967\) 33.8380 1.08816 0.544078 0.839034i \(-0.316879\pi\)
0.544078 + 0.839034i \(0.316879\pi\)
\(968\) 10.6200i 0.341340i
\(969\) 4.44029 + 1.99993i 0.142643 + 0.0642470i
\(970\) 3.43221 0.110202
\(971\) −6.44381 −0.206792 −0.103396 0.994640i \(-0.532971\pi\)
−0.103396 + 0.994640i \(0.532971\pi\)
\(972\) −13.3288 8.08343i −0.427523 0.259276i
\(973\) −32.9167 + 2.10151i −1.05526 + 0.0673713i
\(974\) 16.2562i 0.520881i
\(975\) 25.0069 + 11.2633i 0.800863 + 0.360713i
\(976\) 8.92731i 0.285756i
\(977\) 30.1308i 0.963970i 0.876179 + 0.481985i \(0.160084\pi\)
−0.876179 + 0.481985i \(0.839916\pi\)
\(978\) 2.46851 + 1.11183i 0.0789344 + 0.0355524i
\(979\) 9.62462i 0.307604i
\(980\) −2.32049 + 0.297508i −0.0741254 + 0.00950356i
\(981\) −29.2450 33.0486i −0.933722 1.05516i
\(982\) −24.7150 −0.788689
\(983\) −14.5978 −0.465597 −0.232798 0.972525i \(-0.574788\pi\)
−0.232798 + 0.972525i \(0.574788\pi\)
\(984\) 8.02661 + 3.61523i 0.255879 + 0.115249i
\(985\) 1.23307i 0.0392888i
\(986\) 6.76326 0.215386
\(987\) 12.6989 + 4.77168i 0.404209 + 0.151884i
\(988\) −2.88355 −0.0917379
\(989\) 11.3381i 0.360532i
\(990\) −0.409595 0.462867i −0.0130178 0.0147109i
\(991\) 25.0380 0.795358 0.397679 0.917525i \(-0.369816\pi\)
0.397679 + 0.917525i \(0.369816\pi\)
\(992\) 2.97856 0.0945695
\(993\) −13.9194 + 30.9041i −0.441717 + 0.980711i
\(994\) 0.770951 + 12.0757i 0.0244531 + 0.383017i
\(995\) 3.23047i 0.102413i
\(996\) 8.10090 17.9858i 0.256687 0.569902i
\(997\) 45.0748i 1.42753i −0.700384 0.713766i \(-0.746988\pi\)
0.700384 0.713766i \(-0.253012\pi\)
\(998\) 14.1996i 0.449481i
\(999\) 10.3385 3.21193i 0.327094 0.101621i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 966.2.f.c.461.9 yes 28
3.2 odd 2 inner 966.2.f.c.461.20 yes 28
7.6 odd 2 inner 966.2.f.c.461.6 28
21.20 even 2 inner 966.2.f.c.461.23 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.f.c.461.6 28 7.6 odd 2 inner
966.2.f.c.461.9 yes 28 1.1 even 1 trivial
966.2.f.c.461.20 yes 28 3.2 odd 2 inner
966.2.f.c.461.23 yes 28 21.20 even 2 inner